Powers of i
We now want to simplify certain expressions involving powers of i. To do so,
we first see how to simplify powers of i. Simplifying powers of i can be done
by using the fact that i2 = -1 and expressing the given power of i in terms of
even powers, and then in terms of powers of . Consider the following:
i,
i2 = -1,
i3 = i2.i = (-1)i = -i,
i4 = (i2)2 = (i2)2.i = (-1)2.i = i,
i5 = i4.i = (i2)2.i = (-1)2.i = i,
Note that the power of i cycle themselves through the values i, -1, -i, and 1.